Coupling of vibrational and translation of a scattered molecule

Based on preliminary estimates, the HCl(v=2→2) and HCl(v=2→1) channels are of a comparable magnitude under the experimental conditions used here. While no detailed study of the survival probability of HCl(v=2) is made, an estimation based on the relative intensities of the REMPI spectra indicate a relatively large vibrational relaxation:

>0.1 (4.6)

It is likely this substantial vibrational relaxation involves coupling to electron hole pairs in the metal. Vibrationallly excited molecules scattering from insulators typically show very small amount of vibrational relaxation, for example NO(v=1) scattered from LiF (001) showed no vibrational relaxation.^69,70 Perhaps more germane is the study of Korolick et al. who saw HCl(v=2→1) vibrational relaxation, in scattering from MgO, only when trapping desorption was the primary scattering mechanism.⁷¹ The HCl/Au(111) system by comparison shows clear vibrational relaxation from HCl(v=2→1) in a direct scattering process. This indicates that the

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vibrational relaxation pathway here is strongly coupled to electron hole pairs. Also mismatch of energy between phonons of Au(118 cm^-1) and the vibrational energy lost in vibrational relaxation HCl(v=2→1) (3000 cm^-1) would mean that the amount of vibrational energy we see transferring to the surface would require the excitation of 12 phonons. Such mulitphonon excitation seems unlikely to be efficient.

Recent unpublished calculations from DH Zhang show the barrier to dissociation on Au(111) to be comparable to the vibrational energy in HCl(v=2). If this is indeed the case then trajectories that sample the reactive transition, but fail to dissociate might undergo vibrational relaxation.

This line of reasoning has been previously used to describe the vibrational excitation of H₂ on Cu(111).⁷²

As shown in Fig. 4.6, at E_i=0.52 eV, the HCl(v=2→1) channel shows a broader and slightly higher translational energy distribution. Similar plots were made for the six additional gas mixtures used in this study.

Figure 4.9 Translational energy distributions for vibrationally elastic HCl(v=2→2), solid lines, and inelastic HCl(v=2→1), dashed lines, scattering at several different translational incidence energies at T_S=300 K.⁵⁰

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For both vibrationally elastic and inelastic channels, the translational energy distribution increases with increasing incidence energy and broadens. Quantitative parameters describing the velocity distributions are listed in Table 4.2 and 4.3.

Previous reports for non-adiabatic vibrational energy transfer at surfaces have indicated that the kinetic energy change of the scattered molecules does not depend on Δv.^8,10 As mentioned in the background section, NO in high vibrational states (v=15) has been scattered from Au surfaces losing large amounts of vibrational energy (~1.5 eV), but no noticeable translational energy change was seen.¹⁰ Previous studies of NO(v=0→1) vibrational excitation also did not show a striking difference in the translational energy distribution between elastic and inelastic scattering.²⁹ This work also showed a zero-threshold for vibrational excitation dependence on incidence energy of translation, compared to a clear threshold for mechanical excitation.³⁰ These results led to the idea that translational energy, although important in the coupling of molecular vibration to surface electrons, was itself a spectator. That is to say, V-T coupling is very weak.

Now compare this spectator view to the results shown for the vibrational relaxation of HCl shown here. At all incidence energies the vibrationally inelastic channel has a translational energy distribution that is slightly broader and more energetic than the vibrationally elastic channel. This is seen in Fig. 4.9. In Fig. 4.10 the average energy for vibrationally inelastic and elastic scattering as a function of incidence energy of translation is plotted.

0.00 0.25 0.50 0.75 1.00 1.25

0.00 0.25 0.50 0.75 1.00

<E

> (eV)

<E

i

> (eV)

Figure 4.10 Final average translational energy of the vibrationally elastic, empty circles, and inelastic, filled circles, plotted as a function of incidence energy of translation. The dot dashed line represents a linear fit <E_s>= 0.44 <E_i>

for the vibrationally elastic case. The solid line represents <E_s>= 0.44 <E_i> + 0.0821 eV for inelastic scattering. The dashed line represents the expected inelastic scattering if all released vibrational energy appeared as translation.⁵⁰

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It is clear from Fig. 4.10 that the spectator view of translational energy in vibrational energy change is not fully observed. Indeed at all incidence energies, 26% of the vibrational energy is coupled to translation. This means that the naïve “spectator” view of the translation of the molecule is not fully correct. Possible mechanisms for this coupling of molecular vibration to translation will be discussed.

An interesting comparison is to H₂ scattering from Pd.⁷³ Here H₂ in v=1 J=1 was shown to relax with a high probability to v=0 J=J′. The velocity of the molecules was measured in a way similar to the HCl translational energy studied here. Sitz et al. argued that the large relaxation probability was indicative of electronically non-adiabatic vibrational relaxation. However a large fraction of the vibrational energy of the scattered H₂ coupled to the translation of the molecule.

In fact more energy from vibration coupled to translation of the molecule than coupled to the surface.⁷³ This indicates that the coupling of molecular vibration to translation is not limited to the HCl/Au(111) system.

One possible explanation is that the difference arises due to steric effects. These can be treated in an analogous fashion to previous work by Kimman who showed that total energy transferred to the system decreased with increased scattered rotational state.⁶⁸ The reasoning was that molecules that scattered from the surface in an orientation that was favorable for rotational excitation were not oriented properly for coupling translational energy to the surface. Kroes et al.

showed that H2 dissociation occurs at different surface sites depending on initial quantum state.^74-76 The extension of this idea to the present work suggests that molecules in orientations more likely undergo vibrational relaxation are also more likely to be in an orientation that retains more of its translational energy upon scattering.

Two aspects of these results make this idea seem unlikely. First, in Fig. 4.6 and 4.9 it can be seen that, especially at low incidence energies of translation, the vibrationally inelastic channel has a non-negligible fraction of molecules with energies that exceed that of the incident beam. Since the scattered translational energy exceeds that of the incident molecules, it would seem that vibrational energy is coupled directly to translation and the difference between vibrationally elastic and inelastic is not caused by molecular orientation effects.

Additionally the difference between vibrationally elastic and inelastic translational energy is independent on incidence energy of translation, ~0.08 eV. If molecular orientation was indeed the driving force behind the translational energy difference seen here, one might expect that the slope of the elastic and inelastic translational energy dependence, shown in Fig. 4.10, would be different and for both of them to extrapolate to the origin. However, in this work the vibrationally inelastic case does not extrapolate to the origin. These two factors indicate that the orientation of the HCl when scattering from the Au(111) surface is not the predominant cause of the translational energy difference between the vibrationally elastic and inelastic scattering channels.

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Another possibility for the T-V coupling is that some molecules undergo vibrational relaxation via an electron mediated process while others undergo a mechanical relaxation. An attempt to fit the scattered translational distributions with a bimodal distribution accounting for these two mechanisms was undertaken.

0.0 0.2 0.4 0.6 0.8 1.0

B

Translational Energy (eV)

P(E) ( a .u .)

A

Figure 4.11 Fitting of scattered vibrationally inelastic HCl(v=2→1) translational energy distributions, at two incidence energies 0.78, A, and 0.32 eV, B, of v=1 J=5 at 300 K surface temperature with two components. The open circles represent experimental measurements, the solid lines fits as described in Appendix I. The dashed lines represent the fitting procedure for a bimodal distribution described in text.

The idea of two competeing mechanisms leading to the increased translational energy seen in the vibrational relaxation channel is a bit unlikely however for two reasons. First no hint of bimodal features is seen at any of the incidence energies, see Fig. 4.5. In addition when a bimodal fitting procedure is applied, see below for details, no evidence of a fast peak with the energy expected in purely mechanical vibrational relaxation is seen.

To demonstrate this I fit data like that in Fig. 4.9 to bimodal translational energy distributions described by:

56 the width and the position of the faster component ₁ and E₀₁ are free parameters. Figure 4.11 displays examples from this analysis for two incidence energies. This bimodal fitting procedure results in a fast component that exhibits a mean scattered translational energy only ~0.026 eV higher than the values reported in Fig. 4.10. This analysis makes us doubt that the molecules undergo two distinctly different mechanisms of vibrational relaxation.

Two more possibilities exist which may lead to this difference in translational energy. One is that in the electronically non-adiabatic vibrational energy transfer a transient ion is formed. If the transient ion lives long enough, its attractive image charge would accelerate the molecule toward the surface. The molecule would then undergo translational energy transfer in the same manner as in the vibrationally elastic case, but at a higher initial translational energy. It would then release the electron back to the surface and fly back as a neutral molecule. One other possibility is that the translation of the molecule is only partially a spectator in vibrational relaxation and vibrational energy couples directly to both the translation of the molecule and the electrons in the surface. It is at present not clear which of these mechanisms is a better description of the results shown here. Comparisons to high level theoretical simulations would be very helpful.

Scattered vibrationally excited molecules were shown to undergo vibrational relaxation at the surface in a direct scattering mechanism. The view of translation as a spectator, in electronically non-adiabatic vibrational energy transfer, was seen to be only partially true. 26% of the molecular vibrational energy lost was transferred to translation, and this was independent of the incidence energy of translation of the molecules. Several mechanisms for this coupling were postulated and their likelihood discussed.